A window through the walls of our classroom. This is an interactive learning ecology for students and parents in my Pre-Cal Math 20S class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

Thursday, November 27, 2008

Today Mr. K went over Quadrilateral Investigation. As Casey said on her scribe post, the properties on the chart : Opposite side are equal, all sides are equal, opposite angle are right angles, consecutive angels are supplementary, diagonals are congruent, diagonals bisect each other, diagonals bisect opposite angles and diagonals are perpendicular to each other.

I hope you don't mind that I'm using your pictures, Casey |D

A parallelogram:

opposite sides are equal

consecutive angles are supplementary

diagonals are congruent

diagonals bisect each other

A trapezoid:

opposite angles are right angles

A rectangle:

opposite sides are equal

opposite angles are right angles

consecutive angles are supplementary

diagonals are congruent

diagonals bisect each other

A rhombus

opposite sides are equal

consecutive angles are supplementary

diagonals bisect each other

diagonals bisect opposite angles

diagonals are perpendicular to each other

A right trapezoid

consecutive angles are supplementary

A square

opposite side are equal

all sides are equal

opposite angle are right angles

consecutive angels are supplementary

diagonals are congruent

diagonals bisect each other

diagonals bisect opposite angles

diagonals are perpendicular to each other

Note that: A square is a special case of a rectangle, as it has four right angles and equal parallel side. It is also a special case of trapezoid, rhombus and parallelogram.

Transversal line is a line that passes through two or more lines at different points.

Later on in the class, Mr. K put us into groups to work on Problem Solving: Geometry 0 & 1 or The Proof is in the Parallelogram. We have to prove that ABRM is a parallelogram

First you have to look at the same sides:Angle A = Angle RAngle B = Angle M

Wednesday, November 26, 2008

Today's class, Mr.Kuropatwa put up 2 questions on the board to start off the class.

A. Find the surface area of a prism.

To find the surface area of a prism you have to find the congruent faces. Opposites that have the same area. Find the area of 2 sides (L*w), adjacent sides (w*h), then the two ends (l*w). Then add the total areas. Therefore the answer for the question should be:

SA = 2(2x3) +2 (5x2) +2 (3+5) = 62units²

B. If we triple all the dimensions, what will the new surface area be...Use the pattern we learned yesterday. Although I forgot what the pattern we learned from yesterday, I should of asked again. Answer for the question is:

9x62 = 558

Later on in the class, Mr.K put us into groups to work on a sheet on Quadrilateral. We had to identify figures of shapes with the proper names, examine each figure and identify properties it has in a chart.

The properties on the chart : Opposite side are equal, all sides are equal, opposite angle are right angles, consecutive angles are supplementary. diagonals are congruent, diagonals bisect each other, diagonals bisect opposite angles, diagonals are perpendicular to each other.

The word supplementary means is 2 angles that add up to 180 degrees.The word congruent means is having the exact equal size and shape.The word bisect means cutting into 2 congruent in halves.

Mr.K talked a little bit about Convex and Concave but we will be learning more about Convex. He also talked about the Trapezoid being a special quadrilateral ; 2 sides 1 pair parallel (//) *Remember the symbol for parallel* A Parallelogram ; 2 pairs opposite sides parallel. For a rectangle, all sides are congruent. Why? Because all sides are equal to 90 degrees.

Hopefully I covered most of today's scribe. Please bear with me though I'm not good at explaining everything. I tried my best! If you did not understand anything .. PLEASE ask questions in class; it will help you and everyone. :)

Yesterday we started the class of with finding the surface area and volume of each:

a. Sphere

To find the surface area of each sphere, you need to use the formula: 4pr²(p= pi)

Sphere 1:4p(1)² = 4p14x1xp = 4p

Sphere 2:4p(2)² = 4p44x4xp = 16p

Sphere 3:4p(3)² = 4p94x9xp = 36p

After doing this, you should notice a pattern or a relationship between the spheres above. The end result multiplied by pi have a perfect square in it. By noticing the pattern, you can jump to a sphere that has a radius of 10 instead of doing the formula one after another, after another and so on.For example, if your trying to find the volume of a sphere that has a radius of 10, I think you have to square the radius and then multiply it by 4, after doing that you multiply it by pi or leave it with the pi sign beside it as your final answer.*(This is where I personally feel lost, I am not sure how to explain it, hopefully this will help a little. I believe there is more to it, but this is where I am stuck.)*

Now you have to find the volume of each sphere using the formula: 4/3pr³(p= pi)

Sphere 1:4/3p(1)³ = 4/3p14x1xp divided by 3 = 4p/3

Sphere 2:4/3p(2)³ = 4/3p84x8xp divided by 3 = 32p/3

Sphere 3:4/2p(3)³ = 4/3p274x27xp divided by 3 = 108p/3

b. Cube

Now to find the surface area of each cube you have to use the formula: 6s²

Cube 1:6x1² = 6x1 = 6

Cube 2:6x2² = 6x4 = 24

Cube 3:6x3² = 6x9 = 54

I think there is another pattern, but I am not sure. I have no idea, so I'm just going to leave it as it is.

Now find the volume of each cube using the formula: lwhCube 1:1x1x1 = 1

Cube 2:2x2x2 = 8

Cube 33x3x3 = 27

Since the length, width and the height are all equal, there isn't much to do but to cube the length, width or height.

So most of the class was talking about these questions above and trying to look for a relationship or pattern between them and then we ended the class with sitting in groups trying to figure out these questions below:

1. The area of a shape is 30 cm². If the dimensions of the shape are increased 4 times, what is the area of the new shape?40 x 4² = 480 cm²

2. The volume of a solid is 24cm³. If the dimensions are tripled, what is the new volume?24 x 3³ = 648 cm³

Hopefully this scribe helps whoever did not understand the work we did yesterday, I know I got lost in some parts but I didn't say anything.

Friday, November 21, 2008

Today Mr. K first off talked about the blog, telling us how to write label's properly because if you don't, then you won't get the mark's that you deserved for it. Then he moved on mentioning to us that since we were having difficulty with vocabulary, he now will add onto the blog something that will help us out. This is a site found in the right hand side of the blog with a link called "wordequationswiki" sort of like wikipedia, only this time we could add on word's that we don't understand, ourselves to this site.

Our next unit that we began since we had to move on, is called Geometry. For this unit we need to know volume of a cylinder and sphere formula's. There is also another one that we also need to know about, and it is called the baseball theorem. For example, if you take a baseball and cut all the stitches, and then unfold it, it would have 4 circles. And these 4 cirlcles is what is used to find out the surface of a sphere. This is because if you take the 4 circles multiply it by pie and also multiply the radius by itself 2 times, then you would get the surface of a sphere. Note when multiplying with pie you can't just multiply it with just "3.14". You can't just do that you have to use the whole thing because if you were to use "3.14" that'll only be close to pie unlike if you use the whole thing "3.141592654" your answers will be fully correct.

To get us started with Geometry Mr. K gave us an example:

EX) A sphere fits exactly inside a cylinder. Find the volume of each of the size's of cylinder's with spheres inside them. Is there a relationship or a pattern?

First off you have to find the height of the cylinder. You get the height of the cylinder by the diameter of the sphere. And then once that is settled, for all the 3 size's you plug in the measurement's in the formula. For the volume of cylinder formula this is what it would be like : . For the volume of sphere formula itwould look like this :

Let's start off with the smaller size first to get you help started and to show you how to do it for the other sizes .

First find the volume of the cylinder:

VCYL =

=

== 50.2654

Then find the volume of the sphere inside :

VSPH ==== 33.5103

VCYL == 50.26

VSPH == 33.51

Now do the same method for the medium and the large sizes, which will give us:

Medium Sized:

VCYL =

VSPH =

Large Sized:

VCYL =

VSPH =

In conclusion, using the medium size one, one and a half spheres fit in each cylinders :

===

Our assignment for today was Excercise 23, Questions: All. A reminder on Monday, November 24th 2008, is our test on Radicals and Exponents, so study hard.

You can also try this bottomless quiz (just keep refreshing the page) for finding the volume and surface area of a sphere. Do as many exercises as you feel you need to until you understand the material well.

I know this was a given homework yesterday but I haven't got time. Now, it's not that I'm doing this for the sake of saying, " I did it! " but because I still want to learn how to evaluate and simplify.

My Muddiest point about Radicalsthat i am good at:- Adding radicals-dividing radical- evaluating radicals-and also i can solve any problems of those one, but i am really having trouble withWord Problemsbecause i don't really understand that one, and i hope i will understand

My most muddiest point is around the time you came back.(not to be mean or anything)Personally i just got used to how Dr. Eviatar teaches. So yea thats my most muddiest point.(once again not to be mean or anything)

My personal muddiest point is around the time you came back (not to be mean or anything).I just got used to how Dr. Eviatar taught, so yeah that is my most muddiest point.(once again not to be mean or anything) ^^

Today we had a Pre-Test, these are some the concepts that was included in the Pre-Test.

Rational Numbers

*Can be written as a fraction

*Fractions*Whole Numbers

*Mixed Numbers

*Decimals that end.

*Decimals With a Pattern.

Irrational Number*Cannot be written as a Fraction*Decimals with no end/repeating/pattern.

Radical Operations:Adding/Subtracting:

When you have the same radicand/ike terms, you just simply add them together.

For Example:

---------------------------------------------------------------------------------------When both radicands does not have the same value you might consider factoring the number so it can have the same value.

For Example:

------------------------------------------------------------------------------------------*When a problem has same radicand but does not have the same root, you cannot add them together because they are not like terms.

For Example:

______________________________________________________________

Multiplying:

Dont forget to use FOIL whe multiplying.

---------------------------------------------------------------------------------------Be careful when subtracting after multiplying! Only add the like terms.Also don't forget that there's always a one before the root.____________________________________________________

RationalizingThe denominator is a sum of 3+√y, so we multiply numerator and denominator by the difference 3 - √y.------------------------------------------------------------------------------------The denominator is a difference of √7 - √5, so we multiply numerator and denominator by the sum√7 - √5